What is the solution for y^{''}-3y^'+2y=2x^2+1 ?

The solution for y^{''}-3y^'+2y=2x^2+1 is y=c_{1}e^{2x}+c_{2}e^x+x^2+3x+4

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y^{''}-3y^'+2y=2x^2+1

y^{^{''}} - 3 y^{^{'}} + 2 y = 2 x^{2} + 1

y = c_{1} e^{2 x} + c_{2} e^{x} + x^{2} + 3 x + 4

Solution steps

y^{''} (x) - 3 y^{'} (x) + 2 y = 2 x^{2} + 1

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{x} + x^{2} + 3 x + 4

y = c_{1} e^{2 x} + c_{2} e^{x} + x^{2} + 3 x + 4

y^{^{''}} + 2 y^{^{'}} + y = e^{- x} sin (x)

\frac{d ^{2} x}{d t ^{2}} + 16 x = 1 + 2 sin (4 t)

y^{^{''}} - 4 y = 2 x - sin (x)

y^{^{''}} + y^{^{'}} - 2 y = 5

\frac{d ^{2} y}{d x ^{2}} + 9 y = x e^{2 x} + sin (3 x)

What is the solution for y^{''}-3y^'+2y=2x^2+1 ?
The solution for y^{''}-3y^'+2y=2x^2+1 is y=c_{1}e^{2x}+c_{2}e^x+x^2+3x+4